Connectivity coding for symmetric meshes

Abstract

The encoding method includes the steps of receiving a polygon mesh including a plurality of faces and a plurality of vertices, dividing the polygon mesh into a left half-mesh and a right half-mesh by a plane, extracting the left half-mesh including a first plurality of vertices within and to the left of the polygon mesh, remapping the plurality of faces to represent a new vertex order to generate a plurality of remapped faces, extracting the plurality of remapped faces, compressing the left half-mesh with a codec, predicting the positions of a second plurality of vertices on the right half-mesh using symmetry-based prediction on the compressed left half-mesh, and connecting the left half-mesh and the right half-mesh.

Description

[Technical Field]

[0001] Cross-reference of related applications This application claims priority to U.S. Provisional Patent Application No. 63 / 409,938, filed on 26 September 2022, and U.S. Patent Application No. 18 / 312,722, filed on 5 May 2023, the disclosures thereof being incorporated herein by reference in their entirety.

[0002] This disclosure relates to a set of advanced video coding techniques. More specifically, this disclosure relates to symmetry-based mesh coding by dividing a mesh by planes to which vertices and edges are added. [Background technology]

[0003] Advanced three-dimensional (3D) world representations enable more immersive forms of interaction and communication. To achieve the realism of 3D representations, 3D models have become more sophisticated than ever before, and a considerable amount of data is linked to the creation and consumption of these 3D models. 3D meshes are widely used in immersive 3D model content.

[0004] A 3D mesh can consist of several polygons that describe the surface of a volumetric object. Dynamic mesh sequences can require a large amount of data because the mesh sequence can contain a significant amount of information as it changes over time. Therefore, efficient compression techniques are needed to store and transmit such content.

[0005] VMesh is the current MPEG standard for compressing static and dynamic meshes. Current VMesh reference software separates the input mesh into a simple base mesh and displacement vectors, which are coded separately.

[0006] Symmetry is a property of a geometric object when it is mapped to itself through an operation. In Euclidean metrics, the group of symmetry transformations is called Euclidean isometric transformations, consisting of reflection, translation, rotation, and combinations thereof. Of all these properties, reflective symmetry, or bilateral symmetry, is the most common symmetry that exists in both the biological and non-biological worlds. In a reflection-symmetric mesh, every point and edge corresponds one-to-one through the plane of symmetry.

[0007] The reflection symmetry plane of a mesh can be detected using a simple method involving principal component analysis (PCA) or a more advanced technique using deep learning. Surface reflection symmetry occurs when only the surface of the mesh exhibits reflection symmetry, but not at the xyz points or vertices. Therefore, in this situation, a one-to-one mapping may not be available. [Overview of the project] [Means for solving the problem]

[0008] According to one or more embodiments, a video encoding method performed by at least one processor includes the step of receiving a polygon mesh containing a plurality of faces and a plurality of vertices. The method further includes the step of dividing the polygon mesh into a left half-mesh and a right half-mesh by a plane. The method further includes the step of extracting the left half-mesh containing a first plurality of vertices located in the faces and to the left of the polygon mesh. The method further includes the step of remapping the plurality of faces to represent a new order of vertices in order to generate a plurality of remapped faces. The method further includes the step of extracting the plurality of remapped faces. The method further includes the step of compressing the left half-mesh with a codec. The method further includes the step of predicting the positions of a second plurality of vertices on the right half-mesh using symmetry-based predictions for the compressed left half-mesh. The method further includes the step of connecting the left half-mesh and the right half-mesh.

[0009] According to one or more embodiments, the device includes at least one memory configured to store program code, and at least one processor configured to read the program code and operate as instructed by the program code. The program code includes an receiving code configured to cause at least one processor to receive a polygon mesh containing a plurality of faces and a plurality of vertices. The program code further includes a separation code configured to cause at least one processor to separate the polygon mesh into a left half-mesh and a right half-mesh by a plane. The program code further includes a first extraction code configured to cause at least one processor to extract a left half-mesh containing a first plurality of vertices in the face and to the left of the polygon mesh. The program code further includes a remapping code configured to cause at least one processor to remap a plurality of faces to represent a new order of vertices in order to generate a plurality of remapped faces. The program code further includes a second extraction code configured to cause at least one processor to extract a plurality of remapped faces. The program code further includes a compression code configured to cause at least one processor to compress the left half-mesh by a codec. The program code further includes prediction code configured to cause at least one processor to predict the positions of a second set of vertices on the right half-mesh using symmetry-based predictions for a compressed left half-mesh. The program code further includes connection code configured to cause at least one processor to connect the left half-mesh and the right half-mesh.

[0010] According to one or more embodiments, a non-temporary computer-readable medium storing instructions, the instructions, when executed by at least one processor in an encoder, causes at least one processor to receive a polygon mesh containing a plurality of faces and a plurality of vertices. The instructions further cause at least one processor to separate the polygon mesh into a left half-mesh and a right half-mesh by a plane. The instructions further cause at least one processor to extract a left half-mesh containing a first plurality of vertices located in and to the left of the faces of the polygon mesh. The instructions further cause at least one processor to remap the plurality of faces to represent a new order of vertices in order to generate a plurality of remapped faces. The instructions further cause at least one processor to extract the plurality of remapped faces. The instructions further cause at least one processor to compress the left half-mesh by a codec. The instructions further cause at least one processor to predict the positions of a second plurality of vertices on the right half-mesh using symmetry-based predictions for the compressed left half-mesh. The instructions further cause at least one processor to connect the left half-mesh and the right half-mesh.

[0011] Further features, properties, and various advantages of the disclosed subject matter will become clearer from the detailed description and accompanying drawings below. [Brief explanation of the drawing]

[0012] [Figure 1] This is a schematic diagram of a block diagram of a communication system according to an embodiment of the present disclosure. [Figure 2] This is a schematic diagram of a block diagram of a streaming system according to an embodiment of the present disclosure. [Figure 3] This figure shows symmetric vertices and connectivity predictions according to embodiments of the present disclosure. [Figure 4] This figure shows an example of an added vertex and face according to an embodiment of the present disclosure. [Figure 5]An operation flowchart showing steps executed by a program for symmetry-based mesh coding by dividing a mesh by planes with vertices and edges added according to an embodiment of the present disclosure. [Figure 6] A diagram of a computer system suitable for implementing an embodiment of the present disclosure.

Embodiments for Carrying Out the Invention

[0013] The following detailed description of the exemplary embodiments refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements.

[0014] The foregoing disclosure provides examples and explanations, but is not intended to be exhaustive or to limit the embodiments to the exact forms disclosed. Modifications and variations are possible in light of the above disclosure or may be obtained from practice of the implementation forms. Further, one or more features or components of one embodiment may be incorporated into or combined with other embodiments (or one or more features of other embodiments). Additionally, in the operation flowcharts and descriptions provided below, understand that one or more operations may be omitted, one or more operations may be added, one or more operations may be performed (at least partially) simultaneously, and the order of one or more operations may be interchanged.

[0015] It will be apparent that the systems and / or methods described herein may be implemented in different forms of hardware, firmware, or combinations of hardware and software. Actual dedicated control hardware or software code used to implement these systems and / or methods is not limiting to the embodiments. Therefore, the operation and behavior of the systems and / or methods are described herein without reference to specific software code, and it is understood that software and hardware may be designed to implement the systems and / or methods based on the descriptions herein.

[0016] Even if certain combinations of features are described in the claims and / or disclosed herein, these combinations are not intended to limit the disclosure of possible embodiments. In fact, many of these features may be combined in ways not specifically described in the claims and / or disclosed herein. Each dependent claim listed below may depend directly on only one claim, but the disclosure of possible embodiments includes each dependent claim in combination with all other claims in the set of claims.

[0017] Any element, action, or instruction used herein should not be construed as important or essential unless expressly stated otherwise. Furthermore, where used herein, the articles “a” and “an” are intended to include one or more items and may be used interchangeably with “one or more.” When only one item is intended, the term “one” or similar wording is used. Also, terms such as “has,” “have,” “having,” “include,” and “including” as used herein are intended to be open-ended terms. Additionally, the phrase “based on” is intended to mean “at least partially based on” unless otherwise specified. Furthermore, expressions such as “at least one of [A] and [B]” or “at least one of [A] or [B]” should be understood as including only A, only B, or both A and B.

[0018] Throughout this specification, any reference to “one embodiment,” “embodiment,” or similar language means that certain features, structures, or characteristics described in relation to the embodiment shown are included in at least one embodiment of the present solution. Therefore, the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may all, though not necessarily, refer to the same embodiment.

[0019] Furthermore, the features, advantages, and characteristics described herein may be combined in any suitable manner in one or more embodiments. Those skilled in the art will recognize, in light of the description herein, that the disclosure may be implemented without one or more of the specific features or advantages of a particular embodiment. In other examples, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments of the disclosure.

[0020] Mirror symmetry is a common feature of meshes, especially computer-generated meshes. Symmetry is used to compress symmetrical meshes. Vertices are divided into left and right halves on a plane of symmetry. The left half is encoded by mesh coding, and the right half is encoded by symmetry prediction and displacement coding.

[0021] The proposed methods may be used separately, in any order, or combined, and may be applied to polygon meshes. A polygon mesh can refer to a 3D mesh containing several polygons that describe the surface of a volumetric object. Information about the vertices of a polygon mesh in 3D space and how those vertices are connected may define each polygon and is called connectivity information. Vertex attributes such as color and normals may be associated with mesh vertices. It has been proposed to encode connectivity for symmetry-based mesh coding by predicting symmetric connectivity and handling cross-symmetric plane connectivity. A method for dividing planes by adding vertices is presented.

[0022] Referring to Figures 1 and 2, one or more embodiments of the Disclosure for implementing the encoding and decoding structures of the Disclosure are described.

[0023] Figure 1 illustrates a simplified block diagram of a communication system 100 according to one embodiment of the present disclosure. The system 100 may include at least two terminals 110, 120 interconnected via a network 150. In the case of unidirectional data transmission, the first terminal 110 may locally decode video data, which may include mesh data, to transmit to the other terminal 120 via the network 150. The second terminal 120 may receive the coded video data from the other terminal via the network 150, decode the coded data, and display the restored video data. Unidirectional data transmission may be common in media delivery applications, etc.

[0024] Figure 1 shows a second pair of terminals 130, 140 provided to support the bidirectional transmission of coded video, which may occur, for example, during a video conference. In the case of bidirectional data transmission, each terminal 130, 140 may code video data captured at its local location for transmission to the other terminal via the network 150. Each terminal 130, 140 may also receive coded video data transmitted by the other terminal, decode the coded data, and display the restored video data on a local display device.

[0025] In Figure 1, terminals 110-140 may be, for example, servers, personal computers, and smartphones, and / or any other type of terminal. For example, terminals (110-140) may be laptop computers, tablet computers, media players, and / or dedicated video conferencing equipment. Network 150 represents any number of networks that transmit coded video data between terminals 110-140, including, for example, wired and / or wireless communication networks. Communication network 150 may exchange data over circuit-switched channels and / or packet-switched channels. Typical networks include telecommunications networks, local area networks, wide area networks, and / or the Internet. For the purposes of this description, the architecture and topology of network 150 may not be important to the operation of this disclosure unless described below herein.

[0026] Figure 2 illustrates an example of a video encoder and video decoder configuration in a streaming environment as an example of an application of the subject matter of disclosure. The subject matter of disclosure may also be used in other video-enabled applications, such as video conferencing, digital television, and storage of compressed video on digital media including CDs, DVDs, and memory sticks.

[0027] As shown in Figure 2, the streaming system 200 may include a capture subsystem 213 which includes a video source 201 and an encoder 203. The streaming system 200 may further include at least one streaming server 205 and / or at least one streaming client 206.

[0028] The video source 201 may, for example, create a stream 202 containing a 3D mesh and metadata associated with the 3D mesh. The 3D mesh may consist of several polygons describing the surface of a volumetric object. For example, the 3D mesh may include multiple vertices in 3D space, each vertex being associated with 3D coordinates (e.g., x, y, z). The video source 201 may include, for example, a 3D sensor (e.g., a depth sensor) or 3D imaging technology (e.g., one or more digital cameras) and a computing device configured to generate a 3D mesh using data received from the 3D sensor or 3D imaging technology. The sample stream 202 may have a higher data volume compared to the encoded video bitstream and may be processed by an encoder 203 coupled to the video source 201. The encoder 203 may include hardware, software, or a combination thereof to enable or implement aspects of the subject matter of the disclosure, as will be described in more detail below. The encoder 203 may also further generate an encoded video bitstream 204. The encoded video bitstream 204 may have a lower data size compared to the uncompressed stream 202 and may be stored on the streaming server 205 for later use. One or more streaming clients 206 may access the streaming server 205 and retrieve a video bitstream 209 which may be a copy of the encoded video bitstream 204.

[0029] The streaming client 206 may include a video decoder 210 and a display 212. The video decoder 210 may, for example, decode a video bitstream 209, which is an input copy of an encoded video bitstream 204, and create an output video sample stream 211 that can be rendered on the display 212 or other rendering device (not shown). In some streaming systems, the video bitstreams 204, 209 may be encoded according to a specific video coding / compression standard.

[0030] According to one or more embodiments, a general framework for compressing symmetric connectivity is described. Assuming that a symmetric mesh M having n vertices and m faces has a symmetric face p: ax + by + cz = d, then vertices v in M i :[x i ,y i ,z i ] can be classified as a left vertex, a right vertex, or an in-face vertex. Correspondingly, face

number

[0031] [Table 1]

[0032] num(·) represents the number of elements in a set, abs(·) is the absolute value operator, and τ inplane is the threshold for finding in-face vertices. To encode a symmetric mesh that has both vertices and faces, several steps are taken as follows:

[0033] In some embodiments, the in-plane and left vertices are retained, V K =V I ∪V L (1) n J Assume there are n in-plane vertices and n L left vertices. By extracting the half-mesh, the vertices have new indices from 1 to n J +n L . All right vertices are removed and are assumed to have new indices from n J +n L +1 to n. Thus, the mapping from the old index i to the new index j can be represented by the operator j = P(i).

[0034] In some embodiments, the faces are remapped to represent the order of the new vertices.

Number

[0035] In some embodiments, it is expected that the left face and the intersection face are retained. However, the intersection face includes the removed right vertices. Thus, it cannot be directly compressed. The method of handling face extraction is given in later embodiments.

[0036] In some embodiments, the half-mesh is compressed by a codec such as Draco. Signaling of the symmetry plane and additional information is required. For the right vertices, additional displacement coding can be performed.

[0037] In some embodiments, the mesh coding may not need to maintain the order of the vertices. Thus, the reordering process may be applied first using the left vertices and then the in-plane vertices. The symmetry prediction of the l-th left vertex v l returns the r-th right vertex v r as follows. v r =SymPred(v l ,p),vl ∈V L (3) In the formula, SymPred(·) represents the symmetry operator. The symmetry prediction is applied only to the left vertex, as shown in Figure 3.

[0038] All predicted right vertices are given by the index of their corresponding left-symmetric pair, and n L +n I It has an offset. r = l + n L +n I (4)

[0039] Furthermore, the normal vector of the right face is opposite to that of the left face. Therefore, the prediction of the right-sided plane is reversed in the order of the predicted vertices, as follows:

number

[0040] Flip{·} is an operator used to reverse the order of elements within a set.

[0041] In some embodiments, the left side and the predicted right side need to be connected in order to complete the mesh reconstruction. Methods for connecting intersecting faces are given in later embodiments.

[0042] In one or more embodiments, a method is proposed for dividing a mesh by a plane. The method is used to handle intersecting faces in face extraction by adding vertices. Before performing symmetry extraction, new vertices and edges at the intersection of the intersecting symmetry plane and the symmetry plane are added to the input mesh. In this way, there are no longer any intersecting faces, and therefore it is not necessary to signal and connect the meshes on both sides. A diagram of these added vertices and edges is given in Figure 4.

[0043] The method for deriving new vertices and faces is given as follows:

[0044] [Table 2]

[0045] Calculation PlaneLineCollision(v i ,v i+1 ,p) is a plane p and two vertices v i , v i+1 The goal is to find the point of collision between them.

[0046] In some embodiments, the surface is f=[id1,...,id K This is the index of the vertices in a wavefront format like ],

number

[0047] [Table 3]

[0048] Figure 5 is a flowchart of an exemplary process 500 for symmetry-based mesh coding by dividing the mesh by planes to which vertices and edges are added. In some implementations, one or more process blocks in Figure 5 may be performed by any of the elements described above.

[0049] As shown in Figure 5, process 500 may include a step of receiving a polygon mesh containing multiple faces and multiple vertices (block 510).

[0050] As further shown in Figure 5, process 500 may include the step of dividing the polygon mesh in half by a plane (block 520).

[0051] As further shown in Figure 5, process 500 may also include the step of extracting the left half of the polygon mesh, the left half of the mesh containing a first number of vertices that are in the face and on the left side of the polygon mesh (block 530).

[0052] As further shown in Figure 5, process 500 may include the step of remapping multiple faces to represent a new order of vertices in order to generate multiple remapped faces (block 540).

[0053] As further shown in Figure 5, process 500 may include a step of extracting multiple remapped faces (block 550).

[0054] As further shown in Figure 5, process 500 may include a step of compressing the left half-mesh by the codec (block 560).

[0055] As further shown in Figure 5, process 500 may include the step of predicting the positions of a second set of vertices on the right half-mesh using symmetry predictions based on the compressed left half-mesh (block 570).

[0056] As further shown in Figure 5, process 500 may include a step of connecting the left half-mesh and the right half-mesh (block 580).

[0057] Figure 5 shows an exemplary block of process 500, but in some implementations, process 500 may include additional blocks, fewer blocks, different blocks, or blocks in different arrangements than those shown in Figure 5. Additionally or alternatively, two or more blocks of process 500 may be performed in parallel.

[0058] The techniques described above may be implemented as computer software using computer-readable instructions and may be physically stored on one or more computer-readable media. For example, Figure 6 shows a computer system 900 suitable for implementing a particular embodiment of the present disclosure.

[0059] Computer software can be coded using any suitable machine code or computer language, which may be subjected to mechanisms such as assembly, compilation, and linking to create code that contains instructions that can be executed directly by a computer's central processing unit (CPU), graphics processing unit (GPU), etc., or through interpretation, microcode execution, etc.

[0060] Instructions can be executed on various types of computers or computer components, including, for example, personal computers, tablet computers, servers, smartphones, game consoles, and Internet of Things devices.

[0061] The components shown in Figure 6 for the computer system 900 are examples and are not intended to imply any limitation on the scope of use or functionality of computer software implementing embodiments of the present disclosure. The configuration of the components should not be construed as being dependent on or requiring any one of the components or combinations of components shown in non-limiting embodiments of the computer system 900.

[0062] The computer system 900 may include certain human interface input devices. Such human interface input devices may respond to input from one or more human users, for example, via tactile input (keystrokes, swipes, data glove movements, etc.), audio input (voices, applause, etc.), visual input (gestures, etc.), or olfactory input (not shown). The human interface devices may also be used to capture certain media that are not necessarily directly related to conscious human input, such as audio (voices, music, ambient sounds, etc.), images (scanned images, photographic images, still images, etc., acquired from cameras), and video (two-dimensional video, three-dimensional video including stereoscopic video, etc.).

[0063] The input human interface device may include one or more of the following (only one of each as shown): a keyboard 901, a mouse 902, a trackpad 903, a touchscreen 910, a data glove, a joystick 905, a microphone 906, a scanner 907, and a camera 908.

[0064] The computer system 900 may also include certain human interface output devices. Such human interface output devices may stimulate the senses of one or more human users, for example, through tactile output, sound, light, and smell / taste. Such human interface output devices may include tactile output devices (e.g., tactile feedback via a touchscreen 910, data glove, or joystick 905, although there may also be tactile feedback devices that do not function as input devices). For example, such devices may include audio output devices (e.g., speaker 909, headphones (not shown)), visual output devices (e.g., screen 910 including CRT screens, LCD screens, plasma screens, OLED screens, etc., each with or without touchscreen input functionality, each with or without tactile feedback functionality, some of which may output two-dimensional visual output or output beyond three dimensions through means such as stereographic output, virtual reality glasses (not shown), holographic displays, and smoke tanks (not shown)), and printers (not shown).

[0065] The computer system 900 may also include human-accessible storage devices and associated media, such as optical media including a CD / DVD ROM / RW 920 having a CD / DVD or similar medium 921, a thumb drive 922, a removable hard drive or solid-state drive 923, legacy magnetic media such as tapes and floppy disks (not shown), and specialized ROM / ASIC / PLD-based devices such as security dongles (not shown).

[0066] Those skilled in the art will also understand that the term “computer-readable medium” as used in relation to the subject matter now disclosed does not include transmission media, carrier waves, or other transient signals.

[0067] The computer system 900 may also include interfaces to one or more communication networks. These networks may be, for example, wireless, wired, or optical. The networks may further be local, wide-area, urban, vehicle, and industrial, real-time, or latency-tolerant. Examples of networks include local area networks such as Ethernet and Wi-Fi; cellular networks such as GSM, 3G, 4G, 5G, and LTE; wired or wireless wide-area digital networks such as cable TV, satellite TV, and terrestrial broadcast TV; and vehicle and industrial networks such as CANBus. Certain networks generally require an external network interface adapter connected to a specific general-purpose data port or peripheral bus 949 (e.g., a USB port on computer system 900), while others are commonly integrated into the core of computer system 900 by connection to the system bus, as described below (e.g., an Ethernet interface to a PC computer system, or a cellular network interface to a smartphone computer system). Using any of these networks, computer system 900 may communicate with other entities. Such communication may be unidirectional reception only (e.g., broadcast television), unidirectional transmission only (e.g., CANbus to a specific CANbus device), or bidirectional communication to other computer systems using local area or wide area digital networks. Such communication may include communication to a cloud computing environment 955. Specific protocols and protocol stacks may be used with each of the networks and network interfaces described above.

[0068] The aforementioned human interface device, human-accessible memory device, and network interface 954 can be mounted on the core 940 of the computer system 900.

[0069] The core 940 may include one or more central processing units (CPUs) 941, graphics processing units (GPUs) 942, dedicated programmable processing units in the form of field-programmable gate areas (FPGAs) 943, hardware accelerators 944 for specific tasks, and the like. These devices may be connected via a system bus 948, along with read-only memory (ROM) 945, random access memory 946, and internal mass storage 947 such as an internal hard drive or SSD that is not accessible to the user. In some computer systems, the system bus 948 may be accessible in the form of one or more physical plugs to allow expansion with additional CPUs, GPUs, etc. Peripheral devices may be attached directly to the core's system bus 948 or via a peripheral bus 949. The architecture of the peripheral bus may include PCI, USB, etc. A graphics adapter 950 may be included in the core 940.

[0070] The CPU 941, GPU 942, FPGA 943, and accelerator 944 may, in combination, execute certain instructions that may constitute the aforementioned computer code. This computer code may be stored in ROM 945 or RAM 946. Temporary data may also be stored in RAM 946, while persistent data may be stored, for example, in internal mass storage 947. Fast storage and retrieval to and from any of the memory devices may be enabled by the use of cache memory, which may be closely associated with one or more CPUs 941, GPUs 942, mass storage 947, ROM 945, RAM 946, etc.

[0071] Computer-readable media may contain computer code for performing various computer implementation operations. The media and computer code may be specifically designed and configured for the purposes of this disclosure, or they may be of a type that is well known and available to those skilled in the computer software technology.

[0072] For example, but not limited to, a computer system having the architecture of computer system 900, in particular core 940, may provide functionality as a result of a processor (including CPU, GPU, FPGA, accelerator, etc.) that runs software embodied in one or more tangible computer-readable media. Such computer-readable media may be user-accessible mass storage as described above, as well as media associated with specific storage of core 940, which are of a non-temporary nature, such as the mass storage 947 and ROM 945 inside the core. Software implementing various embodiments of this disclosure may be stored in such devices and run by core 940. The computer-readable media may include one or more memory devices or chips, depending on the specific needs. The software may cause core 940, specifically the processor (including CPU, GPU, FPGA, etc.) within it, to execute specific processes or specific parts of specific processes as described herein, including defining data structures stored in RAM 946 and modifying such data structures according to processes defined by the software. In addition, or as an alternative, a computer system may provide functionality as a result of logic wired to or otherwise embodied in circuits (e.g., accelerator 944) capable of operating to perform a particular process or a particular part of a particular process as described herein, instead of software, or together with software. References to software may also encompass logic, and vice versa, as appropriate. References to computer-readable media may, as necessary, encompass circuits that store software for execution (such as integrated circuits (ICs)), circuits that embody logic for execution, or both. This disclosure encompasses any suitable combination of hardware and software.

[0073] While this disclosure describes several non-limiting embodiments, there are variations, substitutions, and various alternative equivalents that fall within the scope of this disclosure. Therefore, those skilled in the art will understand that numerous systems and methods not expressly shown or described herein can be devised to embody the principles of this disclosure and thus fall within its spirit and scope. [Explanation of Symbols]

[0074] 100 Communication Systems 110 First terminal 120 Second terminal 150 Networks 200 Streaming Systems 201 Video Sources 202 streams 203 Encoder 204 Encoded video bitstream 205 Streaming Servers 206 Streaming Clients 209 video bitstreams 210 Video Decoders 211 Output video sample stream 212 displays 213 Capture Subsystem 500 processes 900 Computer Systems 901 Keyboard 902 Mouse 903 Trackpad 905 Joystick 906 Microphone 907 Scanner 908 Camera 909 Speaker 910 Touchscreen 920 CD / DVD ROM / RW 921 Medium 922 Thumb Drive 923 Solid State Drive 940 cores 941 Central Processing Unit (CPU) 942 Graphics Processing Unit (GPU) 943 Field-Programmable Gate Area (FPGA) 944 Hardware Accelerators 945 Read-only memory (ROM) 946 random access memory 947 Internal large capacity storage 948 System Bus 949 Local buses 950 Graphics Adapter 954 Network Interface 955 Cloud computing environment

Claims

1. A video encoding method performed by at least one processor, wherein the method is The steps include receiving a polygon mesh containing multiple faces and multiple vertices, The steps include dividing the aforementioned polygon mesh into a left half-mesh and a right half-mesh by a plane, A step of extracting the left half-mesh which includes a first number of vertices located in the face and to the left of the polygon mesh, To generate multiple remapped faces, the steps include: remapping the multiple faces to represent a new order of vertices; The steps include extracting the multiple remapped surfaces, The steps include compressing the left half-mesh using a codec, The steps include predicting the positions of a second set of vertices on the right half-mesh using a symmetry-based prediction for the compressed left half-mesh, The steps of connecting the left half-mesh and the right half-mesh. Methods that include...

2. The method according to claim 1, further comprising the step of determining the displacement of the second plurality of vertices.

3. The method according to claim 1, further comprising the step of reordering the first plurality of vertices.

4. The method according to claim 1, wherein each of the plurality of faces is represented by a set of indices of the corresponding vertices.

5. The set of indices for the corresponding vertices describes the connectivity between the multiple faces, The method according to claim 4, wherein the connectivity is divided into a left face, a right face, or a cross-plane of symmetry.

6. The method according to claim 5, further comprising the step of adding new vertices and new edges to the polygon mesh at the intersection of one or more intersecting planes of symmetry with the plane.

7. The aforementioned symmetry prediction is, The steps include adding an offset to the index of each of the multiple vertices on the right half-mesh, The steps include: reversing the prediction of one or more faces on the right half-mesh in the order of the predicted vertices; The method according to claim 1, further comprising:

8. An apparatus configured to perform the method described in any one of Claims 1 to 7.

9. A computer program for causing a computer to perform the method described in any one of claims 1 to 7.

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